The local principle of large deviations for compound Poisson process with catastrophes

2018/06/19 by A. V. Logachov, Logachov, A., O. Logachova +3
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #60F10 #60F15 #60J27 #Diffusion and Search Dynamics #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1806.07459

openalex publication_date 2018/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The continuous time Markov process considered in this paper belongs to a class of population models with linear growth and catastrophes. There, the catastrophes happen at the arrival times of a Poisson process, and at each catastrophe time, a randomly selected portion of the population is eliminated. For this population process, we derive an asymptotic upper bound for the maximum value and prove the local large deviation principle.

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